Forward error correction scheme for data channels using universal turbo codes

ABSTRACT

A method of providing forward error correction for data services uses a parallel concatenated convolutional code which is a Turbo Code comprising a plurality of eight-state constituent encoders wherein a plurality of data block sizes are used in conjunction with said Turbo Code. A variation uses the method in a cellular radio system. Another variation uses the method in both forward and reverse likes of a cellular radio system.

This is a divisional application of U.S. patent application Ser. No.10/156,372, filed May 28, 2002 now U.S. Pat. No. 6,665,829, which is adivisional application of U.S. patent application Ser. No. 09/235,582,filed Jan. 22, 1999, now U.S. Pat. No. 6,430,722.

This application claims priority under 35 U.S.C. § 119(e) of the filingdates of U.S. Provisional Application No. 60/072,368, filed Jan. 23,1998, No. 60/074,932, filed Feb. 17, 1998, No. 60/075,742, filed Feb.23, 1998, and No. 60/076,464, filed Mar. 2, 1998.

BACKGROUND OF THE INVENTION

The present invention relates to error correction in datacommunications, and more particularly, to forward error correction(FEC). Even more particularly, the present invention relates theselection and use of optimal Turbo Codes in high performance datacommunication systems, such as emerging third generation terrestrialcellular mobile radio and satellite telephone systems, for whichflexibility in supporting a wide range of system requirements withrespect to transmission data rates, channel coding rates, quality ofservice measures (e.g., latency, bit-error rate, frame error rate), andimplementation complexity are highly desirable.

Forward error correction (FEC) is required in terrestrial and satelliteradio systems to provide high quality communication over the RFpropagation channel, which induces signal waveform and spectrumdistortions, including signal attenuation (freespace propagation loss)and multi-path induced fading. These impairments drive the design of theradio transmission and receiver equipment, the design objective of whichis to select modulation formats, error control schemes, demodulation anddecoding techniques and hardware components that together provide anefficient balance between system performance and implementationcomplexity. Differences in propagation channel characteristics, such asbetween terrestrial and satellite communication channels, naturallyresult in significantly different system designs. Likewise, existingcommunication systems continue to evolve in order to satisfy increasedsystem requirements for new higher rate or higher fidelity communicationservices.

In the case of terrestrial cellular mobile radio telephony, AnalogMobile Phone System (AMPS) is an exemplary first generation system; theU.S. IS-136 and European GSM time-division multiple-access (TDMA)standards and the U.S. IS-95 code-division multiple-access (CDMA)standard are second generation systems; and the wideband CDMA standardscurrently under development (e.g., CDMA 2000 in the U.S. and UTRA inEurope) are third generation systems.

In the third generation systems the development of flexible, high-speeddata communication services is of particular interest. Desirablefeatures include the ability to perform rate adaptation and to satisfy amultiplicity of quality-of-service (QoS) requirements.

Traditional forward error correction (FEC) schemes for communicationsystems include use of convolutional codes, block codes such asReed-Solomon or BCH codes, and/or concatenated coding schemes.

Turbo Codes are a relatively new class of block codes that have beendemonstrated to yield bit error rate (BER) performance close totheoretical limits on important classes of idealized channels by meansof an iterative soft-decision decoding method.

A Turbo encoder consists of a parallel concatenation of typically twosystematic, recursive convolutional codes (“constituent codes”)separated by an interleaver that randomizes the order of presentation ofinformation bits to the second constituent encoder with respect to thefirst constituent encoder. The performance of a Turbo Code depends onthe choice of constituent codes, interleaver, information block size(which generally increase with higher data rates), and number of decoderiterations. For a particular Turbo Code, in which the constituent codesare fixed, one can ideally adjust the block size and number of decoderiterations to trade-off performance, latency, and implementationcomplexity requirements. As the block size changes, however, a newinterleaver matched to that block size is required.

In a CDMA network with synchronized base stations, the forward linkchannels (from base station to user terminal) can be designed to beorthogonal, using, for example, Walsh-Hadamard spreading sequences. Thisis generally not possible, however, for reverse link channels (from userterminal to base station), which therefore operate asynchronously usingspreading sequences that are only quasi-orthogonal. Thus, the reverselinks in a synchronous CDMA network typically experience moreinterference and therefore may require stronger FEC (via lower ratecodes) than the forward link channels do.

In an asynchronous CDMA network, the forward and reverse link channelsare more similar in terms of interference levels, so it is possible touse a common FEC scheme (or at least more similar FEC schemes) on thetwo links.

The flexibility and high performance of Turbo Codes make them apotentially attractive technology for sophisticated data communicationsservices. It is therefore desirable to identify Turbo Codes and Turbocoding FEC schemes that best match diverse service requirements withrespect to data rates and coding rates while minimizing implementationcomplexity.

The present invention advantageously addresses the above and other needsby providing methods for designing and using universally optimized TurboCodes.

SUMMARY OF THE INVENTION

The present invention advantageously addresses the needs above as wellas other needs by providing an approach for designing universalconstituent codes of Turbo Codes providing optimal performance inconjunction with a variety of different interleaver depths and TurboCode rates.

The present invention is characterized, in its most basic form as amethod of providing forward error correction for data services using aparallel concatenated convolutional code (PCCC) which is a Turbo Codecomprising of a plurality of eight-state constituent encoders wherein aplurality of data block sizes are used in conjunction with said TurboCode.

In one variation, the method of forward error correction further uses auniversal Turbo Code in a cellular mobile radio system.

In one embodiment, the method of forward error correction further uses auniversal Turbo Code in a forward link and a reverse link of a cellularmobile radio system.

Specific universal Turbo Codes, with sets of optimized puncturingpatterns capable of providing several commonly used code rates, areidentified that provide uniformly near-optimal bit error rate and frameerror rate performance over a wide range of information block sizes(hence, data rates) for a set of supported code rates.

Several universal Turbo Codes are identified herein and differ from eachother in terms of: 1) the targeted code rate for which the choice ofconstituent encoders is optimized; and 2) flexibility with regard to thelowest code rate supported.

A suite of preferred universal Turbo Codes is provided from which aTurbo Coding FEC scheme is crafted to best meet the specific designrequirements of a sophisticated data communication system.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other aspects, features and advantages of the presentinvention will be more apparent from the following more particulardescription thereof, presented in conjunction with the followingdrawings wherein:

FIG. 1 is a diagram of a CDMA digital cellular mobile radio systemhardware;

FIG. 2 is a diagram of a CDMA digital cellular mobile radio systemhardware which can implement an embodiment of the present invention;

FIG. 3 is a functional block diagram of a Turbo Code encoder modifiedfor use with the present invention;

FIG. 4 is a functional block diagram of a Turbo Code decoder;

FIGS. 5, 6, 7, 8 illustrate the Bit Error Rate (BER) performance againstsignal-to-noise ratio (SNR) for Turbo Code rate 1/2 and rate 1/3 atInterleaver sizes 1000, 512, and 1024 bits when the Turbo Codes use acandidate constituent code represented by d(D), and n(D);

FIG. 9 illustrates the puncturing schemes studied for optimizing therate 1/4 Turbo Codes;

FIGS. 10, 11, 12 illustrate the BER/FER performance of Constituent Codes#1-3 at a frame size of 512 bits;

FIG. 13 illustrates the BER/FER performance of Constituent Code #1,wherein Constituent Code #1 is at a frame size of 1024 bits, and withconsistent results found at sizes 2048 and 3072 bits, respectively;

FIG. 14 illustrates the BER/FER performance of selected rate 1/4 TurboCodes at frame size 512 bits, with consistent results found at sizes1024, 2048, and 3072 bits, respectively;

FIG. 15 is a comparison of preferred Turbo Code B against otherpuncturing schemes at frame size 512 bits;

FIG. 16 is a lay-out of candidate puncturing patterns for Turbo Codes ofrate 1/3 and rate 1/2 when the constituent codes have rate 1/3;

FIG. 17 illustrates a comparison of rate 1/3 puncturing schemes at framesize 512 bits;

FIG. 18 illustrates rate 1/2 puncturing schemes at frame size 512 bits,with consistent results found at 1024, 2048, and 3072 bits,respectively;

FIG. 19 illustrates a block diagram of a preferred universal constituentencoder for Turbo Codes optimized at code rate 1/2 and rate 1/3 ofvarying Interleaver depths;

FIG. 20 is a functional block diagram for rate 1/4 Turbo Codes optimizedat code rate 1/2 and rate 1/3, including interleaving and puncturing,(rate 1/3, and rate 1/2 use analogous processing);

FIG. 21 illustrates puncturing patterns for rate 3/8 Turbo Codes;

FIG. 22 illustrates rate 3/8 Turbo Codes optimized at code rate 1/2 andrate 1/3 at frame size 512 bits, wherein results are consistent at 1024,2048, and 3072 bits, respectively;

FIG. 23 illustrates puncturing patterns for rate 4/9 Turbo Codes;

FIG. 24 illustrates rate 4/9 Turbo Codes optimized at code rate 1/2 andrate 1/3 using frame size 512 bits;

FIG. 25 is a functional block diagram of a preferred constituent encoderfor Turbo Codes optimized at code rate 1/4;

FIG. 26 illustrates a functional block diagram of a rate 1/4 Turbo Codesoptimized at rate 1/4 including interleaving and puncturing, (rate 1/3and rate 1/2 use analogous processing);

FIG. 27 illustrates puncturing patterns for rate 2/9 Turbo Codes;

FIG. 28 illustrates rate 2/9 Turbo Codes optimized at code rate 1/4using frame size 512 bits;

FIG. 29 illustrates initial puncturing patterns for rate 3/8 TurboCodes;

FIG. 30 illustrates rate 3/8 Turbo Codes optimized at code rate 1/4using frame size 512 bits;

FIG. 31 is a functional block diagram of a preferred universalconstituent encoder for rate 1/2 and rate 1/3 Turbo Codes of varyingInterleaver depths; and

FIG. 32 illustrates a performance comparison of rate 1/4 FER-optimizedTurbo Codes with convolutional codes, at frame size 512 bits, whereinresults are consistent at 1024, 2048, and 3072 bits.

Appendix A is a compilation of figures, collectively referred to hereinas ‘analogous’ figures, curves or simulations or the equivalent.

Corresponding reference characters indicate corresponding componentsthrough out several views of the drawings.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

The following description of the presently contemplated best mode of theinvention is not to be taken in a limiting sense, but is made merely forthe purpose of describing the general principles of the invention. Thescope of the invention should be determined with reference to theclaims.

There are at least two primary aspects of the current invention: 1)forward error correction schemes for data services based on specific‘universal’ Turbo Codes demonstrated to provide near optimal performanceover a wide range of information block sizes and code rates; and 2) themethod by which specific Turbo Codes having the above mentioneddesirable properties can be designed.

Turbo Codes are particularly well-suited to data applications because oftheir excellent error correction capabilities at low signal-to-noise(SNR) ratios and their flexibility in trading off BER and frame errorrate (FER) performance for processing delay. The data services underconsideration in the hereinafter-described embodiments are consistentwith third generation Code Division Multiple Access (CDMA) cellularmobile radio standards currently in development and are typically moredelay-tolerant than low-rate voice services.

The universal Turbo Codes specified herein (and the method of findingsuch codes), however, are also applicable to data services in othercellular mobile radio systems (e.g., the European Time-Division MultipleAccess (TDMA) standard used in GSM) as well as other systems, such assatellite or other wireless communications systems. Several specificTurbo Codes are therefore identified that provide differentoptimizations regarding these requirements. Others would also bepossible.

In order to optimize the performance of Turbo Codes for data services,it is desirable to have a set of “universal” constituent codes thatprovide optimal or nearly optimal performance in conjunction with avariety of different Interleaver depths and Turbo Code rates, thusavoiding tailoring each optimization of particular Turbo Codes.

Referring first to FIG. 1, an exemplary conventional digital cellularmobile radio system using Direct Sequence Code Division Multiple Access(CDMA) Mobile-station-to-base-station (or reverse) link is shown using aconvolutional encoder and a Viterbi decoder. This basic coding andinterleaving can be applied, equally well, to other multiple accesssystems such as the Time Division Multiple Access (TDMA) used in awell-known GSM standard.

FIG. 1 also represents a base-station-to-mobile-station (or forward)link in a cellular mobile radio system. At a transmitting system 100,the system comprises a segmentation processor 104 where user informationbits from a data terminal equipment (not shown) are assembled into fixedlength frames of N bits per frame 106 which are input to a convolutionalencoder 108, (of rate r). Convolutional encoder 108 is coupled to thesynchronization and framing processor 104 which produces N/r codesymbols 110 at an input of a Channel Interleaver 112 coupled to theconvolutional encoder 108. The channel interleaver 112, performspseudo-random shuffling of code symbols 110, and outputs the symbols toa Spread Spectrum modulator 114 coupled to the channel interleaver 112.The Spread Spectrum modulator 114 uses a user specific Transmit PN-codegenerated by a PN converter 116 coupled to the Spread Spectrum modulator114, to produce a spread spectrum signal carried on a RF carrier to amobile RF transmitter 118. Mobile RF transmitter 118 is also coupled tothe Spread Spectrum modulator 114, where a high power amplifier (notshown) coupled to a transmit antenna 120 radiates a signal to a basestation. The techniques of spread spectrum modulation and RFtransmission are well known art to one familiar with spread spectrumcommunication systems.

A signal from a mobile station (‘mobile signal’) received at a basestation Receive antenna 122 is amplified in a Base RF receiver 124 anddemodulated in a Spread Spectrum Demodulator 128, using the same PN-codeused by the mobile RF transmitter 118, to de-spread the signal. Thedemodulated symbols are de-interleaved by a Channel De-Interleaver 130and input to a Viterbi decoder 132. The decoded information bits arereconstructed into receive data blocks 136 and forwarded to the dataterminal equipment at the receive end of the system.

Referring next to FIG. 2, a hardware system for a digital cellularmobile radio system is shown which implements an embodiment of thepresent invention. As before, a reverse link is illustrated although thesame block diagram also represents a forward link. Further, while theCDMA system is used as an example, one familiar with the art wouldconsider the present invention applicable to other systems such as TDMAas well.

Transmit data Blocks 202 from data terminal equipment are segmented andframed at a Segmentation Processor 204 into fixed frame lengths andapplied to a Turbo Code encoder 208. The output from the encoder 208 isfed to a Channel Interleaver 212 to pseudo-randomize the code symbols.The Channel Interleaver 212 provides output to a Spread SpectrumModulator 214 which uses a user specific PN-code from a PN Generator 216to create a spread spectrum signal, carried on a RF carrier to a mobileRF transmitter 218. The channel interleaver 212 is distinguished from aturbo code interleaver (not shown), which is a component of the encoder208. The mobile RF Transmitter 218 coupled to a Transmit Antenna 220uses a high power amplifier (not shown) at the Transmit Antenna 220 toradiate the signal to the base station.

A signal from the mobile station received at a base receive antenna isamplified in a base RF receiver 224 and demodulated in a Spread SpectrumDemodulator 228, which uses the same PN-code as used by the mobile RFtransmitter 218, to de-spread the signal. The demodulated symbols arede-interleaved by the Channel DE-Interleaver 230, and input to the TurboCode decoder 232. Decoded information bits from the Turbo Code decoder232 are reconstructed at a Reconstruction Processor 238 into receivedata blocks 236 and forwarded to the data terminal equipment at thereceive end.

Referring to FIG. 3, the basic structure of a Turbo Code ischaracterized by the parallel concatenation of two simpler constituentcodes at encoder #1 306 and encoder #2 308. Both-constituent encoders,i.e., encoder #1 306 and encoder #2 308 process the same information bitstream 302, but the encoder #2 308 processes information bits 302 in adifferent order than the order in which encoder #1 306 processes theinformation bits 302, since the Interleaver 304 reorders the informationbits in a pseudo-random manner before they reach encoder #2 308 (theconstituent encoder 308). This arrangement reduces the likelihood that asequence of information bits 302 causing encoder #1 306 to produce alow-Hamming weight output 310 would also cause encoder #2 308 to do thesame with its output 314, which makes possible the excellent performanceof Turbo Codes.

Both encoders 306, 308 produce, in addition to the information bits 302(also referred to as systematic bits 302), parity bits 310, 314 whichare punctured by puncturer 312 to achieve a desired overall Turbo Coderate. It is also possible to puncture systematic bits.

The constituent codes of a Turbo Code are usually systematic, recursiveconvolutional codes. The simplest and most widely known recursiveconvolutional codes have rate 1/2 and transfer function:G(D)=[1,n(D)/d(D)],

-   -   where n(D) and d(D) are binary polynomials specifying the feed        forward and feedback connections of the encoder, respectively.

The rate of a Turbo Code is changed by changing the selection of outputbits 310, 314 for puncturing or transmitting. In all the cases herein, a“1” indicates transmitting; a “0” indicates puncturing.

FIG. 3 also shows how two possible puncturing patterns result frompuncturer 312. Alternately puncturing the parity bits between encoder306 and 308 result in a Turbo Code rate r=1/2. Transmitting all of theparity bits at the two encoders 306, 308 produces a code rate r=1/3.

It is not possible to achieve Turbo Code rates lower than 1/3 withouteither increasing the number of constituent encoders or increasing thenumber of output parity bits per constituent encoder. The latter isusually preferred in order to reduce implementation complexity. In thiscase, one considers a rate 1/3 systematic, recursive convolutional codewith transfer function:G(D)=[1,n ₁(D)/d(D),n ₂(D)/d(D)]

Using two such constituent codes provides any Turbo Code rate between1/5 and 1 through puncturing, or deleting.

Turbo Codes are decoded using iterative decoding methods, as shown inthe block diagram of FIG. 4.

Each of the constituent codes are decoded separately using likelihoodestimates of the other constituent decoder 406 or 416 as ‘a priori’information. The constituent decoder 406, 416 must be of asoft-input/soft-output type, such as the Maximum A Posteriori (MAP)algorithm, the sub-optimal Soft-Output Viterbi Algorithm (SOVA), orvariations. After both constituent decoders have processed the data, theprocess can be repeated.

In practice, the turbo decoders 406, 416 are usually limited to a fixednumber of iterations consistent with the implementation complexity andperformance objectives of the system.

FIG. 4 is a general block diagram of a turbo decoder. Soft informationregarding the information bits 404, parity bits for the first encoder402, and parity bits of the second encoder 402′ are received from thedemodulator. First, a first decoder 406 uses received information bits404 and received parity bits 402 to produce a soft decision 408 oninformation bits. The soft decision 408 is interleaved by an interleaver412, the output of which is soft decision 414. Soft decision 414 is fedto a second decoder 416 as a priori information.

The second decoder 416 accepts the soft decision 414 described above andproduces an improved soft decision 420 on information bits which arethen interleaved by an interleaver 422 and fed to the first decoder 406as a priori information. The whole process is repeated as many times asdesired. Final output 420 is obtained by making hard decisions or thesoft decisions out of the first or second decoder.

In accordance with the present invention, a single mother Turbo Code andvarious puncturing patterns are sought to derive uniformly good codesfor various code rates and information block sizes.

A methodology for determining universal constituent codes is developedby first limiting the initial pool of possible universal constituentcodes in accordance with trade-off studies between performance andimplementation complexity. In accordance with the present invention,performance studies using different state codes have shown thateight-state constituent codes provide a good performance trade-off.

Universal constituent codes are first optimized according to the primarycode rate of the targeted application. For example, in the case of CDMAdata communications, separate optimizations can be done for the forwardand reverse links since the reverse links usually require lower coderates for higher coding gain.

The following steps, more fully described below, are used to produceTurbo Codes optimized for rate 1/2 and rate 1/3:

-   -   1) select candidate systematic rate 1/2 constituent encoders        with transfer function of the form [1, n(D)/d(d)], where d(D) is        a primitive polynomial and n(D) starts with 1 and ends with D³;    -   2) determine a Turbo Code rate 1/2 and rate 1/3 test puncturing        pattern to apply to output data encoded by two rate 1/2        constituent encoders;    -   3) form all possible rate 1/2 and rate 1/3 Turbo Codes by        combining each rate 1/2 constituent code pair with the test        patterns;    -   4) evaluate a relative BER performance of all possible rate 1/2        and rate 1/3 Turbo Codes at a fixed Interleaver length;    -   5) select from the group of mother pairs, a subgroup of        candidate pairs for building optimized Turbo Codes based upon a        best overall BER performance;    -   6) evaluate another relative BER performance of a Turbo Code        group comprising the subgroup of candidate pairs punctured with        the rate 1/2 and rate 1/3 puncturing patterns at a plurality of        other Interleaver depths;    -   7) select from the Turbo Code group, a universal code pair which        has another best overall relative BER for the Interleaver        depths; and    -   8) encode data with a rate 1/2 or rate 1/3 Turbo Code comprising        the selected universal code pair, at a first and a second        encoder, the encoders similar and an Interleaver feeding bits        into the second encoder, wherein the bits are ordered        differently before entering each encoder.

Once generated, best Turbo Codes of lower rates such as 1/4, which arecompatible with the rate 1/2 and 1/3 Turbo Codes determined by the abovesteps, can also be determined.

Rate 1/2 Constituent Codes

The following describes how rate 1/2 constituent codes are determined inone embodiment.

First, a list of candidate eight-state, rate 1/2 constituent codepolynomials are determined.

Table 1 lists the determined denominator polynomials d(D) and numeratorpolynomials n(D) in octal notation. There are twelve constituent codecandidates considered for initial screening purposes.

TABLE 1 Candidate 8-State Constituent Encoders of Rate 1/2 NumeratorDenominator Polynomial Polynomial n(D) d(D) (octal (octal notation)notation) 11 13 11 15 11 17 13 11 13 15 13 17 15 11 15 13 15 17 17 11 1713 17 15

Each of the twelve (12) polynomials is expressed in octal form in Table1, and has a corresponding binary and polynomial notation. The binaryequivalent, for example of octal 13, is binary 1011. Binary 1011corresponds to a polynomial d(D)=D⁰(1)+D¹(0)+D²(1)+D³(1)=1+D²+D³.

Next, the candidate Turbo Codes are simulated with an interleaver sizeof 1000 bits and three decoder iterations. The preliminary screening,which results are shown in FIG. 5 and FIG. 6, evaluates the Bit ErrorRate (BER) versus Ebi/No performance of all candidate Turbo Codes ofrate 1/2 and rate 1/3, as described above. Measurement of Ebi/No isequivalent to a relative SNR.

The results of FIG. 5 and FIG. 6 are used to select six (6) codepolynomial pairs. The six (6) candidate universal code pairs, d(D)−n(D),are shown in octal representation the left hand side of Table 2 below.

Next, a corresponding performance of the eight-state Turbo Codes, usingsimulated data with the candidate universal codes at each rate andInterleaver depth, is used to construct Table 2. A sample performancestudy or simulation is shown in FIGS. 7 and 8 showing selected TurboCodes at an Interleaver depth of 512 bits for rate 1/2 and rate 1/3.

Table 2 below shows the approximate SNR loss for simulated data due tousing a non-optimized code at rates 1/2 and 1/3 and Interleaver depthsof 512, 1024, 2048, and 3072 bits.

TABLE 2 Approximate SNR Loss due to Use of Non-Optimized Codes CandidateTurbo Code Rate & Universal Frame Size (bits) Code: 1/2 & 1/2 & 1/2 &1/2 & 1/3 & 1/3 & 1/3 & 1/3 & d(D)-n(D) 512 1024 2048 3072 512 1024 20483072 15-13 0.005 0.00 0.00 0.05 0.10 0.05 0.05 0.10 dB dB dB dB dB dB dBdB 13-15 0.00 0.00 0.00 0.00 0.05 0.05 0.05 005 dB dB dB dB dB dB dB15-17 0.05 0.05 0.00 0.05 0.05 0.05 0.00 0.10 dB dB dB dB dB dB dB dB17-15 0.40 0.50 0.00 0.00 0.05 0.00 dB dB dB dB dB dB 17-13 0.40 0.500.00 0.00 0.00 0.00 dB dB dB db dB dB 13-17 0.05 0.05 0.05 0.00 0.000.10 0.00 0.10 dB dB dB dB dB dB dB dB

In a similar simulation using sixteen-state codes, pairs denoted as31-33 and 31-27 are also shown in sample FIGS. 7 and 8 using four (4)decoder iterations for each sixteen-state code in order to providesimilar complexity comparison with the eight-state codes using eight (8)decoder iterations. Eight-state codes with eight iterations out-performsixteen state codes with four iterations significantly.

With separate simulations, the difference in performance amongst thedifferent interleavers using the above six (6) candidate pairs isobserved to be within 0.05 dB.

Finally, the results of Table 2 show that the following rate 1/2constituent code pair provides the best overall performance across theranges of rates and Interleaver sizes studied:d(D)=1+D ² +D ³ ; n(D)=1+D+D ³,

which represents octal 13 and octal 15, respectively.

In each tabulated case, the performance of Codes 13-15 is within 0.05 dBto the best performing code for that rate and Interleaver size.

This constituent code is thus selected as the basis for Turbo Codedesigns where higher code rates such as 1/2 and 1/3 are dominant.

Rate 1/3 Constituent Code

The following describes how rate 1/3 constituent codes are determined.Similar to the rate 1/2 constituent codes, rate 1/3 constituent codecandidates are identified in Table 3 below for building near optimalTurbo Code rates of 1/4 and 1/5. For this case, the constituent codecandidates for a Turbo Code must have three (3) polynomials instead oftwo (2).

TABLE 3 Candidate Constituent Codes for Optimized Lower-Rate Turbo CodesCC#1 CC#2 CC#3 (Octal 13-15/17) (Octal 15-13/17) (Octal-17-13/15) d(D) =1 + D² + D³ d(D) = 1 + D + D³ d(D) = 1 + D + (Octal 13) (Octal 15) D²+D³ (Octal 17) n₁(D) = 1 + D + D³ n₁(D) = D² + D³ n₁(D) = 1 + D² + D³(Octal 15) (Octal 13) (Octal 13) n₂(D) = 1 +D + D² + D³ n₂(D) = 1 + D +D² + D³ n₂(D) = 1 + D + D³ (Octal 17) (Octal 17) (Octal 15)Optimal Rate 1/4 Turbo Codes

In order to build an overall rate 1/4 Turbo Code, various puncturingschemes must be considered in combination with each constituent codes ofTable 3.

The various puncturing schemes of FIG. 9 are first considered. For arate 1/4 code, a common input information bit or systematic bit, istransmitted by one encoder, along with three (3) of four (4) parity bitsproduced for that input bit, by the two encoders.

The puncturing patterns of FIG. 9, namely 910, 920, 930, and 940, areselected based upon the previously mentioned design principles, to meetstipulated code rates.

Next, each of the three (3) code triads of Table 3 is combined with thefour (4) puncturing patterns 910, 920, 930 and 940, of FIG. 9 to producetwelve (12) possible Turbo Codes to be evaluated with simulated datashown in FIGS. 10 through 12 for a fixed Interleaver depth of 512 bits,for example.

The performance of the twelve (12) Turbo Codes above is then used toselect three (3) best Turbo Code candidates for a more detailedevaluation. Based on the simulation results shown in FIGS. 10 through12, the three (3) best Turbo Code candidates from the twelve (12) are:

-   -   1) Turbo Code A—Constituent Code No. 1 with puncturing Pattern        No. 2;    -   2) Turbo Code B—Constituent Code No. 2 with puncturing Pattern        No. 1; and    -   3) Turbo Code C—Constituent Code No. 3 with puncturing Pattern        No. 1. (Puncturing patterns are selected from FIG. 9, Patterns        910, 920, 930 and 940).

One of the Turbo Codes of codes A through C is next selected for furtherevaluation using simulated data at various additional Interleaver framesizes to verify that the puncturing patterns are also good at otherInterleaver depths.

To confirm the basic methodology, the performance of a Turbo Code basedupon Constituent Code No. 1 (for example) is simulated for frame sizesof 1024, 2048 and 3072 bits. Sample results for BER/FER performance ofCode #1 at 1024 bits is shown in FIG. 13 and confirms the basicmethodology.

Next, FIG. 14 shows the BER/FER performance of simulated data using thethree rate 1/4 Turbo Code Candidates A through C at an Interleaver depthof 512 bits. Consistent results are also achieved at Interleaver sizes1024, 2048 and 3072 bits.

Next, a rate 1/4 Turbo Code candidate is selected from Candidate TurboCodes A through C which provides the best overall performance at allInterleaver depths, in the simulation resulting in FIG. 14 and analogousfigures, such as those depicted in Appendix A. In the case of the rate1/4 Turbo Code, optimization based on BER performance gives a differentresult than optimization based on FER performance. Turbo Code B has thebest overall FER performance and Turbo Code C the best overall BERperformance, for the simulated data. FIG. 15 shows the performance ofTurbo Code B as compared to other puncturing schemes.

Thus, FER optimized Turbo Code B is selected as the basis for the designsince FER performance is usually the more important criteria for dataservices. On the other hand, Turbo Code A can be punctured to give thesame universal Turbo Code identified previously as optimal for rate 1/3(by puncturing all parity bits from the n₂ (D) polynomial). Hence, TurboCode A is the preferred choice for the forward link rate 1/4 codes inorder to have a single universal mother code to implement all of thedifferent code rates.

Although current third generation CDMA encoding primarily concerns rate1/4 channel encoding on the reverse link, rate 1/3 and rate 1/2 channelcoding may be required for some of the highest rate data channels. Auniversal Turbo Code for rate 1/4, rate 1/3, and rate 1/2 can bedesigned, wherein the underlying constituent code is the same and onlythe puncturing pattern used is different. The method for generating thehigher rate Turbo Codes from the rate 1/3 constituent code follows.

Rate 1/3 Turbo Codes Optimized at Rate 1/4

Using the constituent codes derived from the rate 1/4 optimized TurboCodes above, namely Turbo Code B, the rate 1/3 and rate 1/2 Turbo Codecan be designed to be compatible thereto. Thus, Constituent Code No. 2(from Code B) is used as the basis.

FIG. 16 shows seven (7) basic puncturing patterns that can be used toproduce a rate 1/3 Turbo Code and four (4) basic puncturing patterns toproduce a rate 1/2 Turbo Code. The seven (7) rate 1/3 patterns, 1602through 1614 in block diagram 1600, show the consecutive informationpuncturing bit patterns, 1620, 1626, and the four (4) corresponding rowparity bit puncturing patterns 1622, 1624, 1628, and 1630, for the two(2) encoder puncturing block patterns 1616 and 1618. As before, thepattern “1111” shown in row 1620 always transmits all the informationbits from encoder 1. The pattern “0000” of row 1626, always puncturesthe information bits that enter by encoder No. 2. This is because it isnot necessary to transmit the information bit twice. The four (4) rate1/2 puncturing patterns, 1 through 4, identified in FIG. 16 as elementnumbers 1640, 1642, 1644, and 1646, follow the same notation.

Next, in FIG. 17 the BER and FER performance of all possible rate 1/3Turbo Codes simulated with the preferred Constituent Code No. 2 at anInterleaver depth of 512 bits are compared.

Then the two (2) best patterns are selected for further consideration.Next, the performance of these two (2) patterns are compared at furtherInterleaver depths 1024, 2048 and 3078 bits.

In FIG. 17, for example, showing the rate 1/3 puncturing patterns at 512bits, Patterns 2 and 5 are selected based upon curves 1710 and 1720, ashaving the best and next best overall relative FER, respectively.

Pattern 2 is then selected as the best performer over the variousInterleaver depths from further simulations analogous to that of FIG. 17at additional Interleaver sizes for 1024, 2048 and 3072 bits.

Rate 1/2 Turbo Codes Optimized at Rate 1/4

Rate 1/2 Codes can also be optimized at lower rate codes for similarcompatibility as described above. FIG. 18 compares the BER and FERsimulated performance of all the rate 1/2 Turbo Codes at an Interleaverdepth of 512 bits. FIG. 18 is generated using Constituent Code No. 2 andthe four (4) puncturing patterns shown in FIG. 16 for a rate 1/2 TurboCode. Patterns 1 and 4 are determined to be the best based uponsimulated curves 1810 and 1820 for FER performance.

As in the rate 1/3 case optimized at rate 1/4, similar simulation curvesto FIG. 18 are done for Patterns 1 and 4 for Interleaver depths of 1024,2048 and 3072 bits. Based upon the resulting performance/curves Pattern1 is judged to be the best pattern for FER performance.

Preferred Universal Turbo Codes Optimized for Rate 1/2 and 1/3

FIG. 19 shows a block diagram for the constituent encoder optimized inaccordance with the previously described method for Turbo Code rates 1/2and 1/3. FIG. 20 shows the block diagram for the corresponding TurboCode punctured to rate 1/4.

Information bit stream X(t) 1902 is received at a switch 1922, and isprocessed in accordance with several modular adders 1904, 1908, 1920,1910, 1914, 1918, 1919, and several shift registers 1906, 1912 and 1916which are hard-wired to represent two (2) numerator polynomials and onedenominator polynomial.

In FIG. 19, the denominator polynomial d(D), represented in octal 13, ishardwired by the return feedback connection to modular adders 1920 and1904. Before computing, three shift registers 1906, 1912 and 1916 arefirst zeroed.

A first numerator polynomial over a denominator polynomial, representedby “1101”, is hardwired to return output Y_(o)(t) by combining: X(t)1902 with a result of modulator adder 1920 to create a first bit W(t);the modular sum (second bit) of shift register 1906 and W(t) from themodular adder 1908; another zero bit (third bit) indicated by the lackof connection to the register 1912; and the modular sum (fourth bit) ofanother register 1916 and a result of modular adder 1908 from modularadder 1998. The result is Y_(o)(t)=W(t)+S_(o)(t)+S₂(t).

In FIG. 19 a second numerator polynomial over a denominator polynomial,represented by “1111”, is hardwired to return output Y₁(t) by combining:X(t) 1902 with a result of adder 1920 to create a first bit W(t); addingcontents of a further register 1906 to W(t) with the contents of themodular adder 1910 (second bit); adding contents of the register 1912 aresult of adder 1710 with the modular adder 1914 (third bit); and addingcontents of the other register 1916 to a result of adder 1914 withmodular adder 1919 (fourth bit). The result isY₁(t)=W(t)+S_(o)(t)+S₁(t)+S₂(t).

In FIG. 19, the denominator polynomial connections sum the result of theregister 1912 with register 1916 at adder 1920 and then adds it to X(t)1902 at adder 1904. Thus, if modular adder 1904 is the value W(t),register 1906 holds S₀(t), register 1912 holds S₁(t) and register 1916holds S₂(t), and adder 1904 produces W(t)=X(t)+S₁(t)+S₂(t);Y₀(t)=W(t)+S₀(t)+S₂(t); and Y₁(t)=W(t)+S₀(t)+S₁(t)+S₂(t). Thus, theadding is cumulative.

The result of a modular adder is a “1” if the two bits are different,and a “0” if the two bits are the same. Output Y_(o)(t) represents theoutput from numerator Polynomial No. 1 and the denominator polynomial.Output Y₁(t) represents numerator Polynomial No. 2 and denominatorpolynomial.

Initially, S₀=S₁=S₂=0 and the values of the registers 1906, 1912, 1916are shifted from left to right after each clock cycle increment. Thus,S₀(t+1)=W(t); S₁(t+1)=S₀(t), and S₂(t+1)=S₁(t).

The optimal puncturing matrices, shown in FIG. 20, for example, show a“1” for transmitted bits and a “0” for punctured bits. Exemplary FIG. 20shows encoder 2000 with incoming bit X(t) and Interleaver 2002 passinginterleaved bits X′(t) to encoder 2006 to produce output bit X′(t) andparity bits Y_(o) ¹(t), and Y₁ ¹(t). None of the interleaved bits x′(t)are processed in the rate 1/4 encoder 2004, only in the second rate 1/4encoder 2006. Block 2010 shows the puncturing pattern matrices.

More complicated puncturing patterns can be used to achieve otherpossible coding rates. For example, it is possible to select optimalpuncturing patterns to achieve rates 3/8 and 4/9 for Turbo Codesoptimized at rates 1/2 and 1/3; and to achieve rates 2/9 and 3/8 forTurbo Codes optimized at rate 1/4 using the preferred Turbo Codesidentified in the invention.

Similar to FIG. 9 the block diagram for an optimal Turbo Code rate 3/8uses the rate 1/3 mother constituent code of FIG. 20. The encoder forthe constituent code of FIG. 20 is shown in FIG. 19. The puncturingpattern of the rate 3/8 Turbo Codes shown in FIG. 21 punctures 1 out ofevery 6 bits associated with the first numerator polynomial from bothencoders to generate a rate 3/8 Turbo Code.

The second pattern is a extension of the first pattern allowing bothconstituent encoders to have the same rate, namely 6/11. The extensionpattern duplicates the same pattern (matrix) for another three (3) bitsbut moves the location of one transmission bit from one encoder toanother, essentially flipping a “1” in one encoder while flipping a “0”in another encoder at the analogous locations.

FIG. 22 shows the performance of these patterns at an Interleaver depthof 512 bits. Based on these and analogous curves at 1024, 2048, and 3072Interleaver depths, Pattern 2 is chosen to implement the rate 3/8 TurboCodes.

FIG. 23 shows the puncturing patterns selected for rate 4/9 Turbo Codesused with the mother of codes of FIG. 20. Similarly, the second patternis an extension of the first, which allows both constituent encodes tohave the same rate, namely 8/13.

FIG. 24 shows the corresponding performance curves. Pattern 2 is chosento implement the rate 4/9 Turbo Codes.

Thus, one exemplary Turbo Code design, optimized for Turbo Code rates1/2 and 1/3, and universal for all Interleaver depths, has the preferredgenerator polynomials d(D)=1+D²+D³, n₁(D)=1+D+D³, and n₂(D)=1+D+D²+D³.

The preferred puncturing patterns for various code rates are:

-   -   1) Rate 1/4—alternately puncturing parity bits n₁ from one        encoder and n₂ from the same encoder;    -   2) Rate 1/3—puncturing parity bits n₂ from both encoders;    -   3) Rate 1/2—puncturing parity bits n₂ and alternately puncturing        parity bits n₁ from both encoders;    -   4) Rate 3/8—puncturing parity bits n₂ and one out of every 6        parity bits n₁ from both encoders; and    -   5) Rate 4/9—puncture parity bits n₂ and uniformly 3 out of every        8 parity bits n₁ from both encoders.

A simplified version of this code is the universal Turbo Code designconsisting of two constituent encoders having generator polynomialsd(D)=1+D²+D³ and n₁(D)=1+D+D³. (The third polynomial n₂(D) is not used,so the corresponding output is not generated and the encoder blockdiagram is simplified by removing the corresponding connections.) Thisuniversal Turbo Code design supports a minimum code rate equal to 1/3(instead of 1/5). The corresponding preferred set of puncturing patternsare:

-   -   1) Rate 1/3—no puncturing    -   2) Rate 1/2—alternately puncturing parity bits n₁ from both        encoders;    -   3) Rate 3/8—puncturing one out of every 6 parity bits n₁ from        both encoders; and    -   4) Rate 4/9—puncturing uniformly 3 out of every 8 parity bits n₁        from both encoders.        Preferred Universal Turbo Codes Optimized for Code Rate 1/4

The basic block diagram for a preferred constituent encoder is shown inFIG. 25.

FIG. 26 is an encoder block diagram for the preferred rate 1/4 TurboCode. In this case, the second parity bits are alternately punctured bythe two constituent encoders. The preferred puncturing patternsdescribed in earlier section can then be applied to produce rate 1/3 andrate 1/2 Turbo Codes. Other rates can also be supported by identifyingfurther puncturing patterns. This is illustrated by considering rates2/9 and 3/8.

FIG. 27 shows the puncturing patterns for a rate 2/9 Turbo Code. Three(3) different patterns are compared by performance curves in FIG. 28 andanalogous curves, such as those set forth, for example, in Appendix A,showing performance at various frame Interleaver sizes. From a Pattern 2FER curve 2810 and analogous curves, Pattern No. 2 is chosen as theoptimal FER pattern for rate 2/9.

Next, FIG. 29 illustrates six (6) initial screening puncturing patternsfor optimizing a rate 3/8 Turbo Code. The performance of these patternsis simulated at a fixed Interleaver depth of 512 bits. Based on thesimulation, Pattern 5 and Pattern 6 are chosen as the optimal puncturingpatterns for further review.

Two more extension Patterns 7 and 8 of the above Patterns 5 and 6duplicate the same patterns for another three information bits, but movethe location of one of the transmission bits in the parity sequence fromone encoder pattern to another. The extension allows both constituentencoders to have the same rate, namely 6/11 at each encoder.

FIG. 30 shows exemplary performance curves of the above four (4)candidate puncturing Patterns 5, 6, 7 and 8 for rate 3/8 turbo Codes.Based on these results, a Pattern 8 FER curve 3010 and analogous curvessuch as those shown, for example, in Appendix A, demonstrate thatPattern 8 is the optimal puncturing pattern for rate 3/8 Turbo Codes.

Thus, one preferred Universal Turbo Code design optimized for Rate 1/4uses two constituent codes having polynomials d(D)=1+D+D³, n₁=1+D²+D³and n₂=1+D+D²+D³.

The below puncturing patterns are associated optimized patterns aspreviously discussed for Turbo Code rate 1/4 and FER performance formost commonly used Turbo Code rates, where n₁ represents output bitsassociated with a first numerator polynomial, and n₂ represents outputbits associated with a second numerator polynomial:

-   -   1) Rate 1/4—alternately puncture parity bits n₂ from both        constituent encoders.    -   2) Rate 1/3—puncture parity bits n₁ from both constituent        encoders;    -   3) Rate 1/2—puncture parity bits n₂ and every other parity bits        n₁ from both encoders;    -   4) Rate 2/9—puncture every one out of every four parity bits in        n₁ from both encoders; and    -   5) Rate 3/8—puncture parity bits n₁ and one out of every six        parity bits n₂.

These preferred puncturing patterns can also be cyclically shiftedwithout affecting performance. The cyclically shifted patterns areequivalent.

Turbo Coding FEC Schemes for CDMA Data Services

The set of preferred universal Turbo Codes described heretofore in thisinvention provide a suite of flexible high performance channel codesthat are well suited for sophisticated data communication systemsrequiring a variety of low speed and high speed data services. Thissuite of preferred universal Turbo Codes allows the crafting ofdifferent Turbo encoding schemes to meet the specific requirements ofparticular data communication systems.

As a first example, either of the following two FEC schemes iswell-suited and recommended for a synchronous CDMA data communicationsnetwork (such as the third generation CDMA 2000 system currently underdevelopment):

-   -   1) The preferred universal Turbo Code optimized at codes rates        1/2 and 1/3, along with a subset of associated preferred        puncturing patterns, on a forward link; and the preferred        universal Turbo Code optimized at code rate 1/4, along with a        subset of the associated preferred puncturing patterns, on a        reverse link; and    -   2) The preferred universal Turbo Code optimized at codes rates        1/2 and 1/3, along with a subset of associated preferred        puncturing patterns, on both the forward and reverse links.

As a second example, either of the following FEC schemes is well-suitedand recommended for an asynchronous CDMA data communications network(such as the third generation CDMA systems currently in development inEurope and Asia):

-   -   1) The preferred universal Turbo Code Optimized at code rates        1/2 and 1/3, described above, along with a subset of associated        puncturing patterns, on both the forward and reverse links;    -   2) The preferred universal Turbo Code optimized at code rate        1/4, described above, along with a subset of the associated        preferred puncturing patterns, on both the forward and reverse        links; and    -   3) The simplified version of the universal Turbo Code, described        above, along with a subset of the associated preferred        puncturing patterns, on both the forward and reverse links.

The choice of which option to implement depends on the expected dominantcode rate, minimum code rate, and implementation complexity constraintsas well as other system requirements. Of course, additional puncturingpatterns could be designed in accordance with the teachings of thisinvention to provide other Turbo Coding rates.

Other Variations

The universal Turbo Codes identified for high-speed data services areespecially suitable for third generation CDMA cellular mobile radiosystems but could be easily applied to other systems as well.

Well known variations such as Frame Oriented Convolutional Turbo Coding(FOCTC) could also be used in conjunction with the preferred universalconstituent codes and universal Turbo Codes of this invention. Thedesign methodology for selecting universal constituent codes anduniversal Turbo Codes can also be applied to alternate Turbo Codestructures such as those involving more than two constituent encoders,and those involving serial concatenation instead of or in addition toparallel concatenation.

The exemplary preferred puncturing patterns described herein can berefined or modified in various ways by those skilled in the art. Forexample, a cyclic shift of a preferred puncturing pattern offerssubstantially equivalent performance as the preferred puncturing patterndescribed herein. Furthermore, specific data communication systems mayrequire different and additional puncturing patterns to support ratematching. These puncturing patterns may be designed in accordance withthe teachings of the present invention.

While the invention herein disclosed has been described by means ofspecific embodiments and applications thereof numerous modifications invariations could be made thereto by a skilled artisan and withoutdeparting from the scope of the invention set forth in the claims.

1. A data signal, embodied in a carrier wave generated by a wirelesstelephony apparatus, comprising: data that has been encoded by a Turboencoder including a plurality of constituent encoders, each adapted toencode data using a convolutional code, wherein at least one of theplurality of constituent encoders has a transfer function of: G(D)=[1,(1+D+D³)/(1+D²+D³)], wherein D denotes unit delay in presentation ordata bits to the encoder.
 2. The data signal of claim 1, wherein thedata has been encoded using the Turbo encoder with a coding rate equalto 1/3.
 3. A data signal, embodied in a carrier wave generated by awireless telephony apparatus, comprising: data that has been encoded bya Turbo encoder including a plurality of constituent encoders, eachadapted to encode data using a convolutional code, wherein at least oneof the plurality of constituent encoders has a transfer function of:G(D)=[1, (1+D+D³)/d(D)], wherein D denotes unit delay in presentation ofdata bits to the encoder.
 4. The data signal of claim 3, whereind(D)=(1+D²+D³).
 5. The data signal of claim 3, wherein the data has beenencoded using the Turbo encoder with a coding rate equal to 1/3.
 6. Adata signal, embodied in a carrier wave generated by a wirelesstelephony apparatus, comprising: data that has been encoded by a Turboencoder including a plurality of constituent encoders, each adapted toencode data with a convolutional code, wherein at least one of theplurality of constituent encoders has a transfer function of: G(D)=[1,(1+D+D³)/(1+D²+D³), (1+D+D²+D³)/(1+D²+D³)], wherein D denotes unit delayin presentation of data bits to the encoder.
 7. The data signal of claim6, wherein the data has been encoded using the Turbo encoder with thedata rate equal to 1/2.
 8. The data signal of claim 6, wherein the datahas been encoded using the Turbo encoder with the data rate equal to1/3.
 9. The data signal of claim 6, wherein the data has been encodedusing the Turbo encoder with a coding rate equal to 1/4.
 10. A datasignal, embodied in a carrier wave generate by a wireless telephonyapparatus, comprising: data that has been encoded by a Turbo encoderincluding a plurality of constituent encoders, each encoder adapted toencode data with a convolutional code, wherein at least one of theplurality of constituent encoders has a transfer function of: G(D)=[1,n_(x)(D)/d(D), n_(y)(D)/d(D)], wherein n_(x) and n_(y) are polynomialsspecifying feed forward connections and d(D)=(1+D²+D³); wherein Ddenotes unit delay in presentation of data bits to the encoder.
 11. Thedata signal of claim 10, wherein the data has been encoded using theTurbo encoder with a coding rate equal to 1/2.
 12. The data signal ofclaim 10, wherein the data has been encoded using the Turbo encoder witha coding rate equal to 1/3.
 13. The data signal of claim 10, wherein thedata has been encoded using the Turbo encoder with a coding rate equalto 1/4.